I’m assuming since it popped out the material is not glass (which probably would’ve just shattered. You could just forcibly push the bump back into place, may look a bit funny but it would at least sit again.

If you want to make it easier, or try to “reverse” the expansion, you could put the perfume in the freezer. As the liquid cools the parts of it that are in a gaseous state will shrink dramatically, and it will be easier to push it back in. If you leave it in too long though it may go to a solid, which would likely make it expand again (so don’t leave it in overnight or something).

If you’re really tricky you could rig up some kind of air line to the top of the perfume bottle. I would take off the cap it has for this, and remove the perfume, and put some kind of tubing over the opening to the bottle. Then create some kind of suction (you could use your own mouth but be prepared for a huge whiff of perfume if you do), and the decrease in atmosphere in the bottle should make its walls suction in as well. Again doing this too hard could cause further damage to the bottle though.

It looks like it has been permanently disfigured due to the heat and nothing can be done to get it back it shape without melting and recast it.

I would say it is too late for that perfume bottle. :-(

You should decant your perfumes into something glass or metal. Plastic is dubious for keeping perfumes and scents intact. If you can open this container and put it in something else, do it.